Mathematics - Application of Derivative Question with Solution | TestHub

Equation of tangent: $\frac{y-2a\sin \theta }{x-a{\sin }^2\theta }=\frac{1}{\sin \theta }\Rightarrow \frac{x}{-a{\sin }^2\theta }+\frac{y}{a\sin \theta }=1$ Sum of intercepts $=a\left({\sin }^2\theta +\sin \theta \right)$, which is maximum when $\sin \theta =1$ (sum of intercepts) ${}_{\text{max }}=2a$